I see no problem with introducing vegetables at 3 months old (12 weeks), as long as it is not excessive. I'm sure some people will not agree with me, but this is my opinion.
As long as any (safe) food is introduced slowly into the diet, especially for a young bun, then there should be no reason for it to affect them badly. It is true that some rabbits don't do well on certain vegetables, and they get a bit of a runny stool, but you just have to watch out for these and make sure this vegetable is not given, or given in very small quantities.
Carrot is quite high in sugar, so it should be limited to perhaps once a week or so.
A young rabbit (3 months or so) should not have too many veggies in their diet. I would recommend (VERY slowly) introducing different vegetables to them, one at a time, perhaps a pinch of curly kale, or a chunk or so of broccoli, perhaps a few sprigs of rocket.
Then after another few weeks or so, start to increase this until it is the House Rabbit Society guidelines, of a minimum of 2 cups of veggies daily per 6lbs of rabbit.
Pippin got vegetables from 12 weeks old and he was absolutely fine with them. By 4months old he was getting a large bowl of a variety of veggies, and absolutely adored it. It did not change his stool- it had nothing but a good affect on him
Just my :twocents
Jen